Circle tangent question?

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Answer 1 · 2018-04-23T00:29:12

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Let K the tangent RST intersects the smaller circle at K.

Construction

$O,Q;O,SandQ,T$ are joined.

Given ST is tangent to the circle of center O and $angle QST=46^@$

We have alternate $angleQPS=angle QST=46^@$

Hence central $angleQOS=2angleQPS=92^@$

Now in cyclic quadrilateral $OQTS$

Sum of opposite angles

$angleQOS+angleQKS=180^@$

$=>92^@+angleQKS=180^@$

$=>angleQKS=180^@-92^@=88^@<90^@$

So $angleQKS<90^@$ can not be semicircular angle.

Hence $SQ$ is not a diameter.